Polygon Clipping via Spatial Indexing for Viewport Lag Reduction

The patent segments the clipping problem by dividing the set of line segments into two groups: candidate segments (those that may intersect the clip rectangle) and non-candidate segments. This segmentation is achieved by using spatial indexes (R-trees) to identify only those line segments whose bounding boxes intersect with the clip rectangle, thereby reducing the number of segments that need to be checked for intersections from O(m) to a much smaller subset.

The patent performs preliminary actions by pre-computing and storing spatial indexes (R-trees) for the set of line segments before the clipping operation. These indexes organize the line segments based on their spatial locations and bounding boxes, allowing for efficient retrieval of candidate segments during the clipping operation. This preliminary indexing avoids the need to check all line segments during actual clipping.

The patent applies local quality by treating different line segments differently based on their spatial relationship with the clip rectangle. Line segments are categorized into candidate segments (those with bounding boxes intersecting the clip rectangle) and non-candidate segments (those that do not intersect). This local differentiation allows the algorithm to apply intensive intersection checking only to candidate segments while ignoring non-candidate segments, thereby reducing computational complexity while maintaining intersection detection accuracy.

The patent introduces bounding boxes as an intermediary structure between the line segments and the clip rectangle. Instead of directly checking every line segment against the clip rectangle, the algorithm first checks the bounding boxes of line segments against the clip rectangle. This intermediary bounding box check serves as a filtering mechanism that quickly eliminates non-candidate segments before performing the more computationally expensive line segment intersection tests.